[Some of you may have already received this e-mail,
since it arrived just as I killed the list server. mS]

Dear Forum,

recently we had 3 different problems with GAP 3.2 which occured while
running a program written in gap's own language. The things we want
gap to compute seem to be silly, if considered isolated, but in
our program they can only be avoided with difficulties.

1. Character table of the trivial group:
gap> g:=Group(());
Group( () )
gap> CharTable(g);
Error, <G> must not be trivial in
PermGroupOps.LargestMovedPoint( G ) called from
G.operations.DxPreparation( G ) called from
DixonInit( G, opt ) called from
arg[1].operations.CharTable( arg[1] ) called from
CharTable( g ) called from
main loop
brk>

2. The command "DoubleCosets":
gap> g:=Group((1,2),(1,2,3));
Group( (1,2), (1,2,3) )
gap> h:=Subgroup(g,[(1,2)]);
Subgroup( Group( (1,2), (1,2,3) ), [ (1,2) ] )
gap> DoubleCosets(g,h,h);
Error, <G> must operate transitively on <D> in
G.operations.BlocksNoSeed( G, D ) called from
arg[1].operations.Blocks( arg[1], arg[2], [ ], OnPoints ) called from
Blocks( o, PermGroupOps.MovedPoints( o ) ) called from
Extension( bb, a ) called from
PermRefinedChain( G, Reversed( c ) ) called from
..
brk>

3. Character table of groups with strange generators:
gap> g:=Group((2,3,4,5,6),(2,6)(3,5));
Group( (2,3,4,5,6), (2,6)(3,5) )
gap> g.name:="D10";
"D10"
gap> CharTable(g);
Error, operations: product of permutation and boolean is not defined at
if x ^ (el * representatives[x]) in orbitJ ... in
FingerprintPerm( D, D.conjugacyClasses[i].representative, 1, 2, fos, fr
) called from
fun( i ) called from
List( c, function ( i ) ... end ) called from
G.operations.DxPreparation( G ) called from
DixonInit( G, opt ) called from
..
brk>

On a first glance it seems that the domain of operation is {2,3,4,5,6}
instead of {1,2,3,4,5} is the reason for failing. But a similar example
with the dihedral group of order 6 works:
g:=Group((2,3,4),(2,3));
Group( (2,3,4), (2,3) )
gap> CharTable(g);
rec( order := 6, centralizers := [ 6, 2, 3 ], orders :=
[ 1, 2, 3 ], classes := [ 1, 3, 2 ], irreducibles :=
[ [ 1, 1, 1 ], [ 1, -1, 1 ], [ 2, 0, -1 ]
 ], operations := CharTableOps, name := "", powermap :=
[ , [ 1, 1, 3 ], [ 1, 2, 1 ]
 ], automorphisms := Group( () ), text := "origin: Dixon's Algorithm", permuta\
tion := (2,3), group := Group( (2,3,4), (2,3) ) )

Best regards,
Olaf Neisse, Robert Boltje, Universitaet Augsburg, Germany